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Time series prediction is a main research content in time series analysis, and has become a hot research field with great theoretical value and application value. As an extension type of Least Square Support Vector Machine (LS-SVM), recurrent LS-SVM is proposed and applied to chaotic time series prediction. Aimed at the key and difficult research problem on LS-SVM — the selection and construction of kernel functions, a mixed kernel function used to recurrent LS-SVM is constructed through analyzing the existed kernel functions of LS-SVM. Based on Rossler chaotic time series prediction, the parameters of recurrent LS-SVM with mixed kernel are optimized by Genetic Algorithms (GA), and the prediction results are compared with that of recurrent LS-SVM with RBF kernel. The results show that, the prediction accuracy based on recurrent LS-SVM with mixed kernel is apparently higher than that based on recurrent LS-SVM with RBF kernel under the same condition. Compared with recurrent LS-SVM with RBF kernel, recurrent LS-SVM with mixed kernel possesses the better long-time predictive ability by absorbing the advantages of RBF kernel and polynomial kernel function.